Problem: Simplify the following expression: $ q = \dfrac{-9}{n - 9} - \dfrac{-1}{6} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{6}{6}$ $ \dfrac{-9}{n - 9} \times \dfrac{6}{6} = \dfrac{-54}{6n - 54} $ Multiply the second expression by $\dfrac{n - 9}{n - 9}$ $ \dfrac{-1}{6} \times \dfrac{n - 9}{n - 9} = \dfrac{-n + 9}{6n - 54} $ Therefore $ q = \dfrac{-54}{6n - 54} - \dfrac{-n + 9}{6n - 54} $ Now the expressions have the same denominator we can simply subtract the numerators: $q = \dfrac{-54 - (-n + 9) }{6n - 54} $ Distribute the negative sign: $q = \dfrac{-54 + n - 9}{6n - 54}$ $q = \dfrac{n - 63}{6n - 54}$